Fixed point theorems for the sum of (ws)-compact and asymptotically Φ -nonexpansive mappings

Afif Ben Amar; Donal O’Regan; Amel Touati

doi:10.1007/s11784-016-0326-8

Fixed point theorems for the sum of (ws)-compact and asymptotically Φ -nonexpansive mappings

Afif Ben Amar, Donal O’Regan, Amel Touati

Mathematics

Mathematics University of Sfax

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

6 Citations (Scopus)

Abstract

In this paper, we introduce the concept of an asymptotically Φ -nonexpansive operator. In addition, we establish some Krasnoselskiitype fixed point theorems for the sum of two operators A and B, where the operator A is assumed to be (ws)-compact, and B is a (ws)-compact and asymptotically Φ -nonexpansive operator on an unbounded closed convex subset of a Banach space. Also we present Leray–Schauder alternatives and Furi–Pera-type fixed point theorems for the sum of two (ws)-compact mappings.

Original language	English
Pages (from-to)	771-784
Number of pages	14
Journal	Journal of Fixed Point Theory and Applications
Volume	18
Issue number	4
DOIs	https://doi.org/10.1007/s11784-016-0326-8
Publication status	Published - 1 Dec 2016

Keywords

(ws)-compact
asymptotically Φ -nonexpansive
demiclosed
fixed point theorems
measure of weak noncompactness
weakly compact

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10.1007/s11784-016-0326-8

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abstract = "In this paper, we introduce the concept of an asymptotically Φ -nonexpansive operator. In addition, we establish some Krasnoselskiitype fixed point theorems for the sum of two operators A and B, where the operator A is assumed to be (ws)-compact, and B is a (ws)-compact and asymptotically Φ -nonexpansive operator on an unbounded closed convex subset of a Banach space. Also we present Leray–Schauder alternatives and Furi–Pera-type fixed point theorems for the sum of two (ws)-compact mappings.",

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T1 - Fixed point theorems for the sum of (ws)-compact and asymptotically Φ -nonexpansive mappings

AU - Ben Amar, Afif

AU - O’Regan, Donal

AU - Touati, Amel

PY - 2016/12/1

Y1 - 2016/12/1

N2 - In this paper, we introduce the concept of an asymptotically Φ -nonexpansive operator. In addition, we establish some Krasnoselskiitype fixed point theorems for the sum of two operators A and B, where the operator A is assumed to be (ws)-compact, and B is a (ws)-compact and asymptotically Φ -nonexpansive operator on an unbounded closed convex subset of a Banach space. Also we present Leray–Schauder alternatives and Furi–Pera-type fixed point theorems for the sum of two (ws)-compact mappings.

AB - In this paper, we introduce the concept of an asymptotically Φ -nonexpansive operator. In addition, we establish some Krasnoselskiitype fixed point theorems for the sum of two operators A and B, where the operator A is assumed to be (ws)-compact, and B is a (ws)-compact and asymptotically Φ -nonexpansive operator on an unbounded closed convex subset of a Banach space. Also we present Leray–Schauder alternatives and Furi–Pera-type fixed point theorems for the sum of two (ws)-compact mappings.

KW - (ws)-compact

KW - asymptotically Φ -nonexpansive

KW - demiclosed

KW - fixed point theorems

KW - measure of weak noncompactness

KW - weakly compact

UR - https://www.scopus.com/pages/publications/84988709173

U2 - 10.1007/s11784-016-0326-8

DO - 10.1007/s11784-016-0326-8

M3 - Article

SN - 1661-7738

VL - 18

SP - 771

EP - 784

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

IS - 4

ER -

Fixed point theorems for the sum of (ws)-compact and asymptotically Φ -nonexpansive mappings

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Keywords

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