scholarly journals On the generalized asymptotically nonspreading mappings in convex metric spaces

2017 ◽  
Vol 18 (1) ◽  
pp. 117 ◽  
Author(s):  
Withun Phuengrattana
Keyword(s):  
Fixed Points ◽  
Convergence Theorem ◽  
Metric Spaces ◽  
Nonspreading Mapping ◽  
Mann Iteration ◽  
Demiclosed Principle ◽  
New Class ◽  
Convex Metric Spaces ◽  
Nonspreading Mappings ◽  
Nonlinear Mappings

<p>In this article, we propose a new class of nonlinear mappings, namely, generalized asymptotically nonspreading mapping, and prove the existence of fixed points for such mapping in convex metric spaces. Furthermore, we also obtain the demiclosed principle and a delta-convergence theorem of Mann iteration for generalized asymptotically nonspreading mappings in CAT(0) spaces.</p>

scholarly journals Existence of common fixed points via modified mann iteration in convex metric spaces and an invariant approximation result

2010 ◽  
Vol 41 (4) ◽  
pp. 335-348
Author(s):  
G.V.R. Babu ◽  
G.N. Alemayehu
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Convex Metric Space ◽  
Approximation Result ◽  
Mann Iteration ◽  
Invariant Approximation ◽  
Convex Metric Spaces ◽  
Weakly Contractive

We prove the existence of common fixed points for two selfmaps $T$ and $f$ of a convex metric space $X$ via the convergence of modified Mann iteration where $T$ is a nonlinear $f$-weakly contractive selfmap of $X$ and range of $f$ is complete. An invariant approximation result is also proved.

RANDOM COINCIDENCE AND FIXED POINTS FOR WEAKLY COMPATIBLE MAPPINGS IN CONVEX METRIC SPACES

2009 ◽  
Vol 02 (02) ◽  
pp. 171-182 ◽  
Author(s):  
Izmat Beg ◽  
Adnan Jahangir ◽  
Akbar Azam
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Weakly Compatible Mappings ◽  
Compatible Mappings ◽  
Coincidence Points ◽  
Random Coincidence ◽  
Complete Metric Spaces ◽  
Random Fixed Points ◽  
Weakly Compatible ◽  
Convex Metric Spaces

Some new theorems on random coincidence points and random fixed points for weakly compatible mappings in convex separable complete metric spaces have been established. These results generalize some recent well known comparable results in the literature.

scholarly journals On Mann’s Method with Viscosity for Nonexpansive and Nonspreading Mappings in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Nawab Hussain ◽  
Giuseppe Marino ◽  
Afrah A. N. Abdou
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Common Fixed Points ◽  
Nonspreading Mapping ◽  
Type Mapping ◽  
Nonspreading Mappings

In the setting of Hilbert spaces, inspired by Iemoto and Takahashi (2009), we study a Mann’s method with viscosity to approximate strongly (common) fixed points of a nonexpansive mapping and a nonspreading mapping. A crucial tool in our results is the nonspreading-average type mapping.

scholarly journals A New Class of Contraction inb-Metric Spaces and Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Preeti Kaushik ◽  
Sanjay Kumar ◽  
Kenan Tas
Keyword(s):  
Integral Equation ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
New Class ◽  
End Results

A novel class ofα-β-contraction for a pair of mappings is introduced in the setting ofb-metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation.

scholarly journals Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Sy-Ming Guu ◽  
Wataru Takahashi
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Mean Convergence ◽  
Nonspreading Mappings ◽  
Weak Convergence Theorem ◽  
Attractive Point ◽  
Nonlinear Mappings

We study the widely more generalized hybrid mappings which have been proposed to unify several well-known nonlinear mappings including the nonexpansive mappings, nonspreading mappings, hybrid mappings, and generalized hybrid mappings. Without the convexity assumption, we will establish the existence theorem and mean convergence theorem for attractive point of the widely more generalized hybrid mappings in a Hilbert space. Moreover, we prove a weak convergence theorem of Mann’s type and a strong convergence theorem of Shimizu and Takahashi’s type for such a wide class of nonlinear mappings in a Hilbert space. Our results can be viewed as a generalization of Kocourek, Takahashi and Yao, and Hojo and Takahashi where they studied the generalized hybrid mappings.

scholarly journals Fixed Points of Multivalued Nonself Almost Contractions

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Vasile Berinde ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Convex Metric Spaces

We consider multivalued nonself-weak contractions on convex metric spaces and establish the existence of a fixed point of such mappings. Presented theorem generalizes results of M. Berinde and V. Berinde (2007), Assad and Kirk (1972), and many others existing in the literature.

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