scholarly journals Convergence of the Ishikawa Type Iteration Process with Errors of I-Asymptotically Quasi-nonexpansive Mappings in Cone Metric Spaces

2019 ◽  
pp. 1-9
Author(s):  
Ashfaque Ur Rahman ◽  
K. Qureshi ◽  
Geeta Modi ◽  
Manoj Ughade
Keyword(s):  
Fixed Point ◽  
Convex Cone ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Cone Metric Spaces ◽  
Expansive Mapping ◽  
Convex Metric Spaces ◽  
Cone Metric

The goal of this article is to consider an Ishikawa type iteration process with errors to approximate the fixed point of -asymptotically quasi non-expansive mapping in convex cone metric spaces. Our results extend and generalize many known results from complete generalized convex metric spaces to cone metric spaces.

scholarly journals Fixed point theorems of finite family with errors for asymptotically quasi-nonexpansive mappings in convex metric spaces

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 155-166
Author(s):  
Singh Saluja
Keyword(s):  
Fixed Point ◽  
Recent Result ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Finite Family ◽  
Convex Metric Spaces

In this paper, we prove that a multi-step iteration process with errors for a finite family of asymptotically quasi-nonexpansive mappings converges strongly to a common fixed point of the mappings in convex metric spaces. Our results extend and improve the recent result of Kim et al. [9, 10] and many known results.

scholarly journals On Complete Cone Metric Space and Fixed Point Theorem

2011 ◽  
Vol 3 (2) ◽  
pp. 303-309
Author(s):  
J. Mehta ◽  
M. L. Joshi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Weakly Compatible Maps ◽  
Cone Metric Spaces ◽  
Weakly Compatible ◽  
Contractive Type ◽  
Cone Metric

We prove coincidence and common fixed point theorems of four self mappings satisfying a generalized contractive type condition in complete cone metric spaces. Our results generalize some well-known recent results.Keywords: Common fixed point; Complete cone metric space; Weakly compatible maps.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.6475                J. Sci. Res. 3 (2), 303-309 (2011)

scholarly journals On convergence theorems for single-valued and multi-valued mappings in p-uniformly convex metric spaces

2021 ◽  
Vol 37 (3) ◽  
pp. 513-527
Author(s):  
JENJIRA PUIWONG ◽  
◽  
SATIT SAEJUNG ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Fixed Point Set ◽  
Convergence Theorems ◽  
Convex Metric Spaces ◽  
Strict Fixed Point ◽  
Point Set

We prove ∆-convergence and strong convergence theorems of an iterative sequence generated by the Ishikawa’s method to a fixed point of a single-valued quasi-nonexpansive mappings in p-uniformly convex metric spaces without assuming the metric convexity assumption. As a consequence of our single-valued version, we obtain a result for multi-valued mappings by showing that every multi-valued quasi-nonexpansive mapping taking compact values admits a quasi-nonexpansive selection whose fixed-point set of the selection is equal to the strict fixed-point set of the multi-valued mapping. In particular, we immediately obtain all of the convergence theorems of Laokul and Panyanak [Laokul, T.; Panyanak, B. A generalization of the (CN) inequality and its applications. Carpathian J. Math. 36 (2020), no. 1, 81–90] and we show that some of their assumptions are superfluous.

scholarly journals Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces

2020 ◽  
Vol 21 (1) ◽  
pp. 135
Author(s):  
Godwin Amechi Okeke ◽  
Mujahid Abbas
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Cone Metric Spaces ◽  
Nonlinear Operators ◽  
Complex Valued ◽  
Cone Metric

It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces.

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