Relative weighted almost convergence based on fractional-order difference operator in multivariate modular function spaces

2018 ◽  
Vol 113 (3) ◽  
pp. 2201-2220
Author(s):  
Uğur Kadak
Keyword(s):  
Fractional Order ◽  
Difference Operator ◽  
Modular Function ◽  
Function Spaces ◽  
Almost Convergence ◽  
Order Difference ◽  
Weighted Almost Convergence ◽  
Modular Function Spaces

Abstract Korovkin-type theorems in modular spaces and applications

2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Carlo Bardaro ◽  
Antonio Boccuto ◽  
Xenofon Dimitriou ◽  
Ilaria Mantellini
Keyword(s):  
Modular Function ◽  
Function Spaces ◽  
Positive Operators ◽  
Almost Convergence ◽  
Test Functions ◽  
Linear Positive Operators ◽  
Modular Spaces ◽  
Filter Convergence ◽  
Modular Function Spaces ◽  
Korovkin Type Theorems

AbstractWe prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results with respect to an axiomatic convergence, including almost convergence. An extension to non positive operators is also studied. Finally, we give some examples and applications to moment and bivariate Kantorovich-type operators, showing that our results are proper extensions of the corresponding classical ones.

scholarly journals Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
Mary Jacintha ◽  
Abdullah Özbekler
Keyword(s):  
Fractional Order ◽  
Difference Equations ◽  
Difference Operator ◽  
Fractional Operators ◽  
Damping Term ◽  
Fractional Difference ◽  
Riccati Technique ◽  
Order Difference ◽  
Numerical Examples ◽  
Positive Integers

The paper studies the oscillation of a class of nonlinear fractional order difference equations with damping term of the form Δψλzηλ+pλzηλ+qλF∑s=λ0λ−1+μ λ−s−1−μys=0, where zλ=aλ+bλΔμyλ, Δμ stands for the fractional difference operator in Riemann-Liouville settings and of order μ, 0<μ≤1, and η≥1 is a quotient of odd positive integers and λ∈ℕλ0+1−μ. New oscillation results are established by the help of certain inequalities, features of fractional operators, and the generalized Riccati technique. We verify the theoretical outcomes by presenting two numerical examples.

scholarly journals Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 481 ◽  
Author(s):  
Buthinah Dehaish ◽  
Mohamed Khamsi
Keyword(s):  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Modular Function ◽  
Function Spaces ◽  
Mann Iteration ◽  
Modular Spaces ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Modular Function Spaces ◽  
Mann Iteration Process

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci–Mann iteration process, introduced recently by Alfuraidan and Khamsi, defined by

On asymptotic pointwise contractions in modular function spaces

2010 ◽  
Vol 73 (9) ◽  
pp. 2957-2967 ◽  
Author(s):  
M.A. Khamsi ◽  
W.M. Kozlowski
Keyword(s):  
Modular Function ◽  
Function Spaces ◽  
Modular Function Spaces

Modular Function Spaces

2015 ◽  
pp. 47-77
Author(s):  
Mohamed A. Khamsi ◽  
Wojciech M. Kozlowski
Keyword(s):  
Modular Function ◽  
Function Spaces ◽  
Modular Function Spaces

scholarly journals Iterative Approximation of Fixed Point of Multivalued ρ-Quasi-Nonexpansive Mappings in Modular Function Spaces with Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Godwin Amechi Okeke ◽  
Sheila Amina Bishop ◽  
Safeer Hussain Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Point Theory ◽  
Function Spaces ◽  
Initial Value ◽  
Iterative Approximation ◽  
Modular Function Spaces ◽  
Nonlinear Mappings

Recently, Khan and Abbas initiated the study of approximating fixed points of multivalued nonlinear mappings in modular function spaces. It is our purpose in this study to continue this recent trend in the study of fixed point theory of multivalued nonlinear mappings in modular function spaces. We prove some interesting theorems for ρ-quasi-nonexpansive mappings using the Picard-Krasnoselskii hybrid iterative process. We apply our results to solving certain initial value problem.

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