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Metric Spaces Of Non Positive Curvature

Some Results on Fixed Points

Preface On the Semilocal Convergence of Newton's Method Under Unifying Conditions Inequalities and Fixed Points in Menger Convex Metric Spaces Applications of the Perov's Fixed Point Theorem to Delay Integro-Differential Equations On Vector Equilibrium Problems with Multifunctions Fixed Points in Generalised Metric Spaces and the Stability of a Cubic Functional Equation Continuous Selection and Coincidence Theorems on Product G-Convex Space Sensitivity Analysis of Solution Set for a New Class of Generalised Implicit Quasi-Variational Inclusions Fixed Points in Probabilistic-Quasi-Metric Spaces Common Fixed Point Theorems for Condensed Mappings The Strongly Convergence Theorems of Fixed Points for Local Strictly F-Pseudocontractive On Generalised Non-linear Variational Inequalities A Note on a Paper of Hadic and Pap The Ishiwaka and Mann Iteration Methods On Certain Applications of Leray-Schauder Alternate Remarks on Concepts of Generalised Convex Spaces Generic Existence and Non-Existence of Approximate Fixed Points General System of Relaxed g-?-r-Pseudococoercive Non-linear Variational Inequalities and Projection Methods Three-Step Iteration Methods with Errors for Non-expansive Mappings in Uniformly Convex Banach Spaces On Nonnegative Linear Composite Games of NTU-Game Probabilistic Contractor and Non-linear Operator Equations with Set-Valued Operator in Probabilistic Normed Spaces Index.

Fixed Point Theory and Applications

(b) Show that if X is uniformly convex and (xn) ⊂ X such that lim n→∞ ‖xn‖ = 1 and lim n,m→∞ ‖xn + xm‖ = 2, then (xn) is convergent. Proceed as follows. Use the definition to prove first that if all terms in the sequence have unit length, then the sequence is Cauchy. In the general case, let yn = xn/‖xn‖. Prove that lim n,m→∞ ‖yn + ym‖ = 2. Then, combine this with what you have shown already to prove that (xn) must be Cauchy. (c) Prove that if X is uniformly convex and S ⊂ X is closed and convex, then S contains a unique element of minimal norm, that is, a unique s0 ∈ S such that inf s∈S ‖s‖ = ‖s0‖. Proceed as follows. Let d = inf s∈S ‖s‖. Now, use part (b) to construct a

On Uniformly Convex Spaces

We introduce a new iterative process which can be seen as a hybrid of Picard and Mann iterative processes. We show that the new process converges faster than all of Picard, Mann and Ishikawa iterative processes in the sense of Berinde (Iterative Approximation of Fixed Points, 2002) for contractions. We support our analytical proof by a numerical example. We prove a strong convergence theorem with the help of our process for the class of nonexpansive mappings in general Banach spaces and apply it to get a result in uniformly convex Banach spaces. Our weak convergence results are proved when the underlying space satisfies Opial’s condition or has Frechet differentiable norm or its dual satisfies the Kadec-Klee property.

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A Picard-Mann hybrid iterative process

In this paper, we are concerned with the study of an iterative scheme with errors involving two nonexpansive mappings. We approximate the common fixed points of these two mappings by weak and strong convergence of the scheme in a uniformly convex Banach space under a condition weaker than compactness.

Weak and strong convergence of a scheme with errors for two nonexpansive mappings

Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications

In this paper, we get some results on strong and @?-convergence in CAT(0) spaces for an iterative scheme which is both faster than and independent of the Ishikawa scheme. We also obtain some results for two mappings using the Ishikawa-type iteration scheme. The motivation of the present work comes from that of Dhompongsa and Panyanak (2008) [3].

Strong and Δ-convergence of some iterative schemes in CAT(0) spaces

In this paper, using the setting of a generalized metric space, a unique common fixed point of four R-weakly commuting maps satisfying a generalized contractive condition is obtained. We also present example in support of our result.

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Safeer Hussain Khan

Papers

Weak and strong convergence of a scheme with errors for two nonexpansive mappings

A Picard-Mann hybrid iterative process

Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications

Strong and Δ-convergence of some iterative schemes in CAT(0) spaces

Common fixed points of R-weakly commuting maps in generalized metric spaces