Measures of weak noncompactness, nonlinear leray-schauder alternatives in banach algebras satisfying condition (p) and an application

Leray Schauder Type Fixed Point Theorems in RWC-Banach Algebras and Application to Chandrasekhar Integral Equations

“…Remark 3.13. Corollary 3.12 extends Theorem 3.5 in [2] to RWC-Banach algebras. In contrast to Theorem 3.5 in [2], the operator A in our results needs not be regular nor weakly compact and B in our results needs not be weakly compact.…”

“…(2) Corollary 3.12 extend Theorem 3.1 in [2] to RWC-Banach algebras, and relaxing the sequential weak continuity of A and C, by assuming only that A and C satisfy only Condition (H 2 ). In contrast to Theorem 3.1 in [2], the operator A in our results needs not be regular. (3) When C ≡ x 0 for some x 0 ∈ X, Corollary 3.12 extend Theorem 3.2 in [2] to RWC-Banach algebras, and relaxing the sequential weak continuity of A and C, by assuming only that A and C satisfy only Condition (H 2 ).…”

“…(3) When C ≡ x 0 for some x 0 ∈ X, Corollary 3.12 extend Theorem 3.2 in [2] to RWC-Banach algebras, and relaxing the sequential weak continuity of A and C, by assuming only that A and C satisfy only Condition (H 2 ). In contrast to Theorem 3.2 in [2], the operator A in our results needs not be regular.…”

“…The Leray Schauder alternative, one of the most important tools in nonlinear analysis. Many fixed point theorems of Leray Schauder type are obtained on Banach algebras satisfying the condition (P), see [2,7,9,11].…”

Measure of Weak Noncompactness and Fixed Point Theorems in Banach Algebras with Applications

“…The problems of the existence of solutions for an integral equation can then be resolved by searching fixed points for nonlinear operators in a Banach algebra. For this, many researchers have been interested in the case where the Banach algebra is endowed with its strong topology; however, few of them were interested to the existence of a fixed point for mappings acting on a Banach algebra equipped with its weak topology [7][8][9][10][11]; such a topology allows obtaining some generalizations of these results.…”