Mohamed Khamsi
University of Texas at El Paso (UTEP), Mathematical Sciences, Faculty Member
- http://www.drkhamsi.com/publication/publication.htmledit
In this paper we show that the common fixed point set of a commuting family of holomorphic mappings in is either empty or a holomorphic retract.
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ABSTRACT Let (M,d)(M,d) be a complete 2-uniformly convex metric space. Let CC be a nonempty, bounded, closed, and convex subset of MM, and let T:C→CT:C→C be an asymptotic pointwise nonexpansive mapping. In this paper, we prove that the... more
ABSTRACT Let (M,d)(M,d) be a complete 2-uniformly convex metric space. Let CC be a nonempty, bounded, closed, and convex subset of MM, and let T:C→CT:C→C be an asymptotic pointwise nonexpansive mapping. In this paper, we prove that the modified Mann iteration process defined by xn+1=tnTn(xn)⊕(1−tn)xnxn+1=tnTn(xn)⊕(1−tn)xn converges in a weaker sense to a fixed point of TT.
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We introduce and study strong convergence of a general iteration scheme for a finite family of asymptotically quasi-nonexpansive maps in convex metric spaces and CAT(0)CAT(0) spaces. The new iteration scheme includes modified Mann and... more
We introduce and study strong convergence of a general iteration scheme for a finite family of asymptotically quasi-nonexpansive maps in convex metric spaces and CAT(0)CAT(0) spaces. The new iteration scheme includes modified Mann and Ishikawa iterations, the three-step iteration scheme of Xu and Noor and the scheme of Khan, Domlo and Fukhar-ud-din as special cases in Banach spaces. Our results are refinements and generalizations of several recent results from the current literature.
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A unified account of the major new developments inspired by Maurey's application of Banach space ultraproducts to the fixed point theory for non-expansive mappings is given in this text. The first third of the book is devoted to... more
A unified account of the major new developments inspired by Maurey's application of Banach space ultraproducts to the fixed point theory for non-expansive mappings is given in this text. The first third of the book is devoted to laying a careful foundation for the actual fixed point ...
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In this paper we show that the common fixed point set of a commuting family of holomorphic mappings in is either empty or a holomorphic retract.
Research Interests:
ABSTRACT In this work, we introduce a density property in ordered sets that is weaker than the order density. Then, we prove a strong version of a result proved by T. Büber and W. A. Kirk [in: World congress of nonlinear analysts ’92.... more
ABSTRACT In this work, we introduce a density property in ordered sets that is weaker than the order density. Then, we prove a strong version of a result proved by T. Büber and W. A. Kirk [in: World congress of nonlinear analysts ’92. Proceedings of the first world congress, Tampa, FL, USA, August 1992. Berlin: de Gruyter. 2115–2125 (1996; Zbl 0844.47031)], which is a special case of the Brouwer Reduction Theorem, in metric spaces relating completeness and density of ordered sets.
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In this work we define the so-called modulus of noncompact con- vexity in modular spaces. We extend the results obtained in Banach spaces by Goebel and Sekowski while their methods can not be repro- duced as.
• We say that a sequence of functions {f n : D → ℝ} defined on a subset D ⊆ ℝ converges pointwise on D if for each x ∈ D the sequence of numbers {f n(x)} converge. If {f n} converges pointwise on D, then we define f : D → ℝ with f( x ) =... more
• We say that a sequence of functions {f n : D → ℝ} defined on a subset D ⊆ ℝ converges pointwise on D if for each x ∈ D the sequence of numbers {f n(x)} converge. If {f n} converges pointwise on D, then we define f : D → ℝ with f( x ) = limn ®</font
ABSTRACT • We say A ⊂ ℝ is open if for every x ∈ A there exists ε > 0 such that (x − ε, x + ε) ⊆ A. A is closed if its complement A c is open. Similarly a set A in a metric space (M,d) is called open if for each x ∈ A, there exists... more
ABSTRACT • We say A ⊂ ℝ is open if for every x ∈ A there exists ε > 0 such that (x − ε, x + ε) ⊆ A. A is closed if its complement A c is open. Similarly a set A in a metric space (M,d) is called open if for each x ∈ A, there exists an ε > 0 such that B(x;ε) ⊂ A. Here,
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• Let f : D → ℝ and let c be an accumulation point of D. We say that a real number L is a limit of f at c, and write
ABSTRACT • If x belongs to a class A, we write x ∈ A and read as “x is an element of A.” Otherwise, we write x ∉ A.
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• Let (a k) be a sequence of real numbers. We use the notation sn = å</font >k = 0n aks_n \, = \,\sum\limits_{k = 0}^n {a_k } to denote the nth partial sum of the infinite series s¥</font > ... more
• Let (a k) be a sequence of real numbers. We use the notation sn = å</font >k = 0n aks_n \, = \,\sum\limits_{k = 0}^n {a_k } to denote the nth partial sum of the infinite series s¥</font > = å</font >k = 0¥</font > aks_\infty \, = \,\sum\limits_{k = 0}^\infty {a_k } . If the sequence of partial sums (s n) converges to a real number s, we say that the series å</font >k ak\sum\limits_k {a_k } is convergent and we write s = å</font >k = 0¥</font > ak s\, = \sum\limits_{k = 0}^\infty {a_k } \, . A series that is not convergent is called divergent.
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• Let f be a real-valued function defined on an interval I containing the point c. We say f is differentiable at c if the limit