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FIXED POINTS OF WEAKLY K-NONEXPANSIVE MAPPINGS AND A STABILITY RESULT FOR FIXED POINT ITERATION PROCESS WITH AN APPLICATION
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  • SAYANTAN PANJA,
  • Kushal Roy,
  • Marija V. Paunovic,
  • Mantu Saha,
  • Vahid Parvaneh
SAYANTAN PANJA
The University of Burdwan

Corresponding Author:[email protected]

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Kushal Roy
The University of Burdwan
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Marija V. Paunovic
Faculty of Hotel Management and Tourism, University of Kragujevac, 36210 Vrnjacka Banja, Vojvodjanska bb, Serbia
Mantu Saha
The University of Burdwan
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Vahid Parvaneh
Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran

Abstract

In this article, we introduce a new type of non-expansive mapping, namely weakly K-nonexpansive mapping, which is weaker than non-expansiveness and stronger than quasi-nonexpansiveness and prove some weak and strong convergence results, using weakly K-nonexpansive mappings. Also we define weakly (α;K)-nonexpansive mapping and using it prove one stability result for JF-iteration process. Some prominant examples are presented which illustrats the facts. A numerical example is presented to compare the convergence behavior of some known iterative algorithms, for weakly K-nonexpansive mappings. Moreover we show by an example that the class of α-nonexpansive mappings due to Aoyama and Kohsaka and the class of generalized α-nonexpansive mappings due to Pant and Shukla are independent. Finally, our fixed point theorem is applied to obtain solution of a nonlinear fractional differential equation.