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Dhage, Bapurao Chandrabhan Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.1
The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.
A Common Fixed Point Theorem for a Pair of Coincidentally Commuting Mappings in Metric Spaces
Dhage, B.C. ...et al KYUNGPOOK UNIVERSITY 1999 Kyungpook mathematical journal Vol.39 No.2
In this paper two common fixed point theorems are proved for a pair of coincidentally commuting mappings on a metric space satisfying generalized contractive condition which in turn include the fixed point theorems of Dhage [1] as the special cases in metric spaces.
Basic Results in the Theory of Hybrid Casual Nonlinear Differential Equations
DHAGE, BAPURAO CHANDRABHAN Department of Mathematics 2015 Kyungpook mathematical journal Vol.55 No.4
In this paper, some basic results concerning the existence, strict and nonstrict inequalities and existence of the maximal and minimal solutions are proved for a hybrid causal differential equation. Our results generalize some basic results of Leela and Laksh-mikantham [13] and Dhage and Lakshmikantham [10] respectively for the nonlinear first order classical and hybrid differential equations.
Some Nonlinear Alternatives in Banach Algebras with Applications II
Dhage, B.C. Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.2
In this paper a nonlinear alternative of Leray-Schauder type is proved in a Banach algebra involving three operators and it is further applied to a functional nonlinear integral equation of mixed type $$x(t)=k(t,x({\mu}(t)))+[f(t,x({\theta}(t)))]\(q(t)+{\int}_0{^{\sigma}^{(t)}}v(t,s)g(s,x({\eta}\(s)))ds\)$$ for proving the existence results in Banach algebras under generalized Lipschitz and $Carath{\acute{e}}odory$ conditions.
ON EXISTENCE THEOREMS FOR NONLINEAR INTEGRAL EQUATIONS IN BANACH ALGEBRAS VIA FIXED POINT TECHNIQUES
Dhage, B.C. The Youngnam Mathematical Society 2001 East Asian mathematical journal Vol.17 No.1
In this paper an improved version of a fixed point theorem of the present author [3] in Banach algebras is obtained under the weaker conditions with a different method and using measure of non-compactness. The newly developed fixed point theorem is further-applied to certain nonlinear integral equations of mixed type for proving the existence theorems and stability of the solution in Banach algebras.
Nonlinear Functional Boundary Value Problems in Banach Algebras Involving Carathéodories
DHAGE, BAPURAO C. 대한수학회 2006 Kyungpook mathematical journal Vol.46 No.4
In this paper, an existence theorem for a nonlinear two point boundary value problem of second order differential equations in Banach algebras is proved using a nonlinear alternative based on Leray-Schauder alternative.
RANDOM FIXED POINTS OF WEAKLY INWARD MULTIVALUED RANDOM MAPS IN BANACH SPACES
Dhage, B.C.,Shahzad, Naseer Korean Mathematical Society 2003 대한수학회보 Vol.40 No.4
Some random fixed point theorems for weakly inward multivalued random maps are obtained in Banach spaces.
Dhage, Bapurao C. Korean Mathematical Society 2007 대한수학회보 Vol.44 No.2
In this paper, some hybrid fixed point theorems are proved which are further applied to first and second order neutral functional differential equations for proving the existence results for the extremal solutions under the mixed Lipschitz, compactness and monotonic conditions.
Dhage, B.C. Korean Mathematical Society 1999 대한수학회보 Vol.36 No.3
In this paper some common fixed point theorems for pairs of condensing mappings in a Banach space are proved and applications are given to a pair of nonlinear first order ordinary differential equations in Banach spaces for proving the existence of common solution under suitable conditions.