scholarly journals Fixed point theorems in locally convex spaces and a nonlinear integral equation of mixed type

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Fuli Wang ◽  
Hua Zhou
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Mixed Type ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Locally Convex Spaces ◽  
Equation Of Mixed Type ◽  
Locally Convex ◽  
Convex Spaces

scholarly journals Fixed point theorems for countably asymptotically Ф-nonexpansive maps in locally convex spaces and application

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 879-904
Author(s):  
Afif Ben Amar ◽  
Saoussen Derbel
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Locally Convex Spaces ◽  
Nonexpansive Operator ◽  
Nonexpansive Maps ◽  
Asymptotically Nonexpansive ◽  
Continuous Maps ◽  
Locally Convex ◽  
Convex Spaces

In this paper, we introduce the concept of a countably asymptotically ?-nonexpansive operator. In addition, we establish new fixed point results for some countably asymptotically ?-nonexpansive and sequentially continuous maps, fixed-point results of Krasnosel?skii type in locally convex spaces. Moreover, we present Leray-Schauder-type fixed point theorems for countably asymptotically ?-nonexpansive maps in locally convex spaces. Apart from that we show the applicability of our results to the theory of Volterra integral equations in locally convex spaces. The main condition in our results is formulated in terms of the axiomatic measure of noncompactness. Our results improve and extend in a broad sense recent ones obtained in literature.

Fixed point theorems for condensing multimaps on locally -convex spaces

2007 ◽  
Vol 67 (5) ◽  
pp. 1522-1531 ◽  
Author(s):  
Young-Ye Huang ◽  
Tian-Yuan Kuo ◽  
Jyh-Chung Jeng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces

scholarly journals Some Algebraic and topological random fixed point theorems with applications to nonlinear random integral equations

2004 ◽  
Vol 35 (4) ◽  
pp. 321-346 ◽  
Author(s):  
B. C. Dhage
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Mixed Type ◽  
Fixed Point Theorems ◽  
Random Operators ◽  
Random Fixed Point ◽  
Nonlinear Functional ◽  
Monotonicity Conditions ◽  
Random Integral ◽  
Equation Of Mixed Type

In this paper some algebraic and topological random fixed point theorems are proved involving the three random operators on a Banach algebra and they are further applied to a certain nonlinear functional random integral equation of mixed type for proving the existence as well as existence of extremal random solutions under the generalized Lipschizicity, Carath´eodory and monotonicity conditions.

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