Journal of science, engineering and technology, Jun 14, 2024
The purpose of this paper is to briefly study the development of some common fixed point theorems... more The purpose of this paper is to briefly study the development of some common fixed point theorems in semi-metric space. INTRODUCTION Metric fixed point theory is a branch of fixed point theory which has its primary applications in functional analysis. Apart from establishing the existence of a fixed point, it often becomes necessary to prove the uniqueness of the fixed point. Besides, from computational point of view, an algorithm for calculating the value of the fixed point to a given degree of accuracy is desirable. Often this algorithm involves the iteration of the given function. In essence, the question about the existence, uniqueness and approximation of fixed point provide three significant aspect of the general fixed point principle. Among several fixed point theorems, Brouwer's fixed point theorem is well known due to its remarkable application in different fields
Kathmandu University Journal of Science, Engineering and Technology, 1970
In this paper we establish a common fixed point theorem for two pairs of weakly compatible maps i... more In this paper we establish a common fixed point theorem for two pairs of weakly compatible maps in dislocated metric space which generalizes and improves similar fixed point results.
In this paper, we introduce the notion of compatible mappings of type (E) in fuzzy metric space a... more In this paper, we introduce the notion of compatible mappings of type (E) in fuzzy metric space and obtain a common fixed point theorem for self mappings in complete fuzzy metric space with example. Our result generalizes and improves other similar results in literature.
The innovative concept of fuzzy mathematics has become one of the interesting areas of research s... more The innovative concept of fuzzy mathematics has become one of the interesting areas of research since last fifty-five years, which was first introduced by Zadeh in 1965. Many researchers connected the fuzzy concept in different forms of metric spaces. The results about the point sets have discussed, mainly topological properties of sets, connecting with the fuzzy metric space. The propose of this paper is to study the point set topology in fuzzy metric space, especially by introducing the concept of open and closed balls and discuss some of the common properties. Moreover, we introduce the concept of compactness and pre-compactness in fuzzy metric space.
The aim of the present paper is to obtain an answer to an open problem due to Sastry et al. [5] b... more The aim of the present paper is to obtain an answer to an open problem due to Sastry et al. [5] by using the relationship between the continuity and reciprocal continuity of mappings in the setting of control functions which alter distances.
Kathmandu University Journal of Science, Engineering and Technology, 1970
The classical Banach contraction principle in metric space is one of the fundamental results in m... more The classical Banach contraction principle in metric space is one of the fundamental results in metric space with wide applications. And the probabilistic metric space is one of the important generalizations of metric space introduced by Austrian mathematician Karl Menger in 1942. The purpose of this article is to describe different contraction conditions in Probabilistic Metric Space. Also, mention the generalized contraction conditions and interrelationships between contraction conditions.
The purpose of our paper is to obtain a common fixed point theorem for two pairs of self-mappings... more The purpose of our paper is to obtain a common fixed point theorem for two pairs of self-mappings of compatible of type (K) in a complete intuitionistic fuzzy Metric space with example. Our result generalized and improves similar other results in literature.
We introduce the concepts of vague additive groups and vague rings on sub graphs. Vague fields on... more We introduce the concepts of vague additive groups and vague rings on sub graphs. Vague fields on Galio's groups. Also we define the concept of vague vector space on sub graphs.
The main objective of this paper is to study some slokas of Veda(s) and its connection with Moder... more The main objective of this paper is to study some slokas of Veda(s) and its connection with Modern Mathematics, Information Technology relative to conveying message. The message or information delivered through Akashvani during the period of Satya Yuga to Modern (Kali Yuga) period without direct technology at that time.
The aim of this paper is to discuss fixed point notion, kutastha vindu and Vedanta Philosophy and... more The aim of this paper is to discuss fixed point notion, kutastha vindu and Vedanta Philosophy and also to find their interrelationship used in Hindu mythological books.
The aim of the present paper is to establish a common fixed point theorem for semi-compatible pai... more The aim of the present paper is to establish a common fixed point theorem for semi-compatible pair of self maps in a fuzzy metric space which generalizes and improves various well-known comparable results.
This article attempts to explore on contributions of Chandrakala Devi Dhananjaya and analyze her ... more This article attempts to explore on contributions of Chandrakala Devi Dhananjaya and analyze her contributions in the field of Nepalese mathematics to materialize her book 'Shishubodha Tarangini'.
In this paper we obtain common fixed point theorems under the Lipschitz type analogue of a strict... more In this paper we obtain common fixed point theorems under the Lipschitz type analogue of a strict contractive condition by using the notion of R weak commutativity of type (Ag). In the setting of our results, we use the property (E.A) introduced by Aamri and Moutawakil [1] and compare these with the results proved by using the notion of noncompatiblity introduced by Pant [4]. Simultaneously, we provide contractive condition which ensure the existence of a common fixed point; however, the mappings are discontinuous at the common fixed point. We, thus, provide one more answer to the problem of Rhoades [10]. Our theorems extend the results of Pant and Pant (Theorem 2.1 Pant [6]), Pant, R.P. [5, Theorem 2]), Pant Vyomesh [8] and Singh and Kumar [11].
Chemostat is a continuous stirred tank reactor used for continuous microbial biomass production i... more Chemostat is a continuous stirred tank reactor used for continuous microbial biomass production in commercial, medical and other research problems. While modeling real world phenomena through differential equations as backbone of practical problems, we need to introduce various parameters. These parameters may be vague, imprecise and uncertain. To incorporate these uncertainties, the notion of fuzzy differential equations is used in chemostat model as one of the tool. In this paper, we discuss some new results for the stability analysis of chemostat model and the results so obtained are justifiable analytically and verified graphically in fuzzy environment.
Vedic mathematics is found to be very effective and sound for mental calculations in mathematics.... more Vedic mathematics is found to be very effective and sound for mental calculations in mathematics. Sutras and sub sutras have beautiful and striking tricks for fast and easy for mathematical calculations. In this article, we explore on importance of Vedic Mathematics with thematic analysis. Vedic Math provides more systematic, simplified, unified and faster than the conventional system. A significant and interesting invention which has led to various applications in all the disciplines is the development of Vedic Math approach. The importance of Vedic mathematics can be characterized as: 1) mathematical calculations, 2) speed, 3) classic approach, 4) fun and interesting, and 5) individual confidence.
... Kathmandu University Kathmandu, NEPAL e-mail: jhakn@ku.edu.np Abstract: We investigate maxima... more ... Kathmandu University Kathmandu, NEPAL e-mail: jhakn@ku.edu.np Abstract: We investigate maxima and minima of some functionals associated with solutions to Dirichlet problems for elliptic equations. ... Now, by Hardy-Littlewood inequality and (3.1) we find ...
In this paper, we establish a common fixed point theorem for three pairs of self mappings in semi... more In this paper, we establish a common fixed point theorem for three pairs of self mappings in semi-metric space using compatible mappings of type (R) which improves and extends similar known results in the literature.
Journal of science, engineering and technology, Jun 14, 2024
The purpose of this paper is to briefly study the development of some common fixed point theorems... more The purpose of this paper is to briefly study the development of some common fixed point theorems in semi-metric space. INTRODUCTION Metric fixed point theory is a branch of fixed point theory which has its primary applications in functional analysis. Apart from establishing the existence of a fixed point, it often becomes necessary to prove the uniqueness of the fixed point. Besides, from computational point of view, an algorithm for calculating the value of the fixed point to a given degree of accuracy is desirable. Often this algorithm involves the iteration of the given function. In essence, the question about the existence, uniqueness and approximation of fixed point provide three significant aspect of the general fixed point principle. Among several fixed point theorems, Brouwer's fixed point theorem is well known due to its remarkable application in different fields
Kathmandu University Journal of Science, Engineering and Technology, 1970
In this paper we establish a common fixed point theorem for two pairs of weakly compatible maps i... more In this paper we establish a common fixed point theorem for two pairs of weakly compatible maps in dislocated metric space which generalizes and improves similar fixed point results.
In this paper, we introduce the notion of compatible mappings of type (E) in fuzzy metric space a... more In this paper, we introduce the notion of compatible mappings of type (E) in fuzzy metric space and obtain a common fixed point theorem for self mappings in complete fuzzy metric space with example. Our result generalizes and improves other similar results in literature.
The innovative concept of fuzzy mathematics has become one of the interesting areas of research s... more The innovative concept of fuzzy mathematics has become one of the interesting areas of research since last fifty-five years, which was first introduced by Zadeh in 1965. Many researchers connected the fuzzy concept in different forms of metric spaces. The results about the point sets have discussed, mainly topological properties of sets, connecting with the fuzzy metric space. The propose of this paper is to study the point set topology in fuzzy metric space, especially by introducing the concept of open and closed balls and discuss some of the common properties. Moreover, we introduce the concept of compactness and pre-compactness in fuzzy metric space.
The aim of the present paper is to obtain an answer to an open problem due to Sastry et al. [5] b... more The aim of the present paper is to obtain an answer to an open problem due to Sastry et al. [5] by using the relationship between the continuity and reciprocal continuity of mappings in the setting of control functions which alter distances.
Kathmandu University Journal of Science, Engineering and Technology, 1970
The classical Banach contraction principle in metric space is one of the fundamental results in m... more The classical Banach contraction principle in metric space is one of the fundamental results in metric space with wide applications. And the probabilistic metric space is one of the important generalizations of metric space introduced by Austrian mathematician Karl Menger in 1942. The purpose of this article is to describe different contraction conditions in Probabilistic Metric Space. Also, mention the generalized contraction conditions and interrelationships between contraction conditions.
The purpose of our paper is to obtain a common fixed point theorem for two pairs of self-mappings... more The purpose of our paper is to obtain a common fixed point theorem for two pairs of self-mappings of compatible of type (K) in a complete intuitionistic fuzzy Metric space with example. Our result generalized and improves similar other results in literature.
We introduce the concepts of vague additive groups and vague rings on sub graphs. Vague fields on... more We introduce the concepts of vague additive groups and vague rings on sub graphs. Vague fields on Galio's groups. Also we define the concept of vague vector space on sub graphs.
The main objective of this paper is to study some slokas of Veda(s) and its connection with Moder... more The main objective of this paper is to study some slokas of Veda(s) and its connection with Modern Mathematics, Information Technology relative to conveying message. The message or information delivered through Akashvani during the period of Satya Yuga to Modern (Kali Yuga) period without direct technology at that time.
The aim of this paper is to discuss fixed point notion, kutastha vindu and Vedanta Philosophy and... more The aim of this paper is to discuss fixed point notion, kutastha vindu and Vedanta Philosophy and also to find their interrelationship used in Hindu mythological books.
The aim of the present paper is to establish a common fixed point theorem for semi-compatible pai... more The aim of the present paper is to establish a common fixed point theorem for semi-compatible pair of self maps in a fuzzy metric space which generalizes and improves various well-known comparable results.
This article attempts to explore on contributions of Chandrakala Devi Dhananjaya and analyze her ... more This article attempts to explore on contributions of Chandrakala Devi Dhananjaya and analyze her contributions in the field of Nepalese mathematics to materialize her book 'Shishubodha Tarangini'.
In this paper we obtain common fixed point theorems under the Lipschitz type analogue of a strict... more In this paper we obtain common fixed point theorems under the Lipschitz type analogue of a strict contractive condition by using the notion of R weak commutativity of type (Ag). In the setting of our results, we use the property (E.A) introduced by Aamri and Moutawakil [1] and compare these with the results proved by using the notion of noncompatiblity introduced by Pant [4]. Simultaneously, we provide contractive condition which ensure the existence of a common fixed point; however, the mappings are discontinuous at the common fixed point. We, thus, provide one more answer to the problem of Rhoades [10]. Our theorems extend the results of Pant and Pant (Theorem 2.1 Pant [6]), Pant, R.P. [5, Theorem 2]), Pant Vyomesh [8] and Singh and Kumar [11].
Chemostat is a continuous stirred tank reactor used for continuous microbial biomass production i... more Chemostat is a continuous stirred tank reactor used for continuous microbial biomass production in commercial, medical and other research problems. While modeling real world phenomena through differential equations as backbone of practical problems, we need to introduce various parameters. These parameters may be vague, imprecise and uncertain. To incorporate these uncertainties, the notion of fuzzy differential equations is used in chemostat model as one of the tool. In this paper, we discuss some new results for the stability analysis of chemostat model and the results so obtained are justifiable analytically and verified graphically in fuzzy environment.
Vedic mathematics is found to be very effective and sound for mental calculations in mathematics.... more Vedic mathematics is found to be very effective and sound for mental calculations in mathematics. Sutras and sub sutras have beautiful and striking tricks for fast and easy for mathematical calculations. In this article, we explore on importance of Vedic Mathematics with thematic analysis. Vedic Math provides more systematic, simplified, unified and faster than the conventional system. A significant and interesting invention which has led to various applications in all the disciplines is the development of Vedic Math approach. The importance of Vedic mathematics can be characterized as: 1) mathematical calculations, 2) speed, 3) classic approach, 4) fun and interesting, and 5) individual confidence.
... Kathmandu University Kathmandu, NEPAL e-mail: jhakn@ku.edu.np Abstract: We investigate maxima... more ... Kathmandu University Kathmandu, NEPAL e-mail: jhakn@ku.edu.np Abstract: We investigate maxima and minima of some functionals associated with solutions to Dirichlet problems for elliptic equations. ... Now, by Hardy-Littlewood inequality and (3.1) we find ...
In this paper, we establish a common fixed point theorem for three pairs of self mappings in semi... more In this paper, we establish a common fixed point theorem for three pairs of self mappings in semi-metric space using compatible mappings of type (R) which improves and extends similar known results in the literature.
Uploads
Papers by Kanhaiya Jha