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RELATIVE RECIPROCAL VARIATIONAL INEQUALITIES
( Awais Gul Khan ),( Muhammad Aslam Noor Amjad Pervez ),( Khalida Inayat Noor ) 호남수학회 2018 호남수학학술지 Vol.40 No.3
In this paper, we introduce a new class of reciprocal convex set which is called as relative reciprocal convex set. We establish a necessary and sufficient condition for the minimum of the differentiable relative reciprocal convex function. This condi-tion can be viewed as a new class of variational inequality which is called relative reciprocal variational inequality. Using the auxiliary principle technique we discuss the existence criteria for the solu-tion of relative reciprocal variational inequality. Some special cases which are naturally included in our main results are also discussed.
Fractional dynamical systems for variational inclusions
Awais Gul Khan,MUHAMMAD ASLAM NOOR,KHALIDA INAYAT NOOR 호남수학회 2019 호남수학학술지 Vol.41 No.1
In the present paper, we propose some new fractional dynamical systems. These dynamical systems are associated with the variational inclusions involving difference of operators problem. The equivalence between the variational inclusion problems and the fixed point problems and as well as the resolvent equations are used to suggest fractional resolvent dynamical systems and fractional resolvent equation dynamical systems, respectively. We show that these dynamical systems converge $\alpha $-exponentially to the unique solution of variational inclusion problems under fewer restrictions imposed on operators and parameters. Several special cases also discussed.
FRACTIONAL DYNAMICAL SYSTEMS FOR VARIATIONAL INCLUSIONS INVOLVING DIFFERENCE OF OPERATORS
Khan, Awais Gul,Noor, Muhammad Aslam,Noor, Khalida Inayat The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.1
In the present paper, we propose some new fractional dynamical systems. These dynamical systems are associated with the variational inclusions involving difference of operators problem. The equivalence between the variational inclusion problems and the fixed point problems and as well as the resolvent equations are used to suggest fractional resolvent dynamical systems and fractional resolvent equation dynamical systems, respectively. We show that these dynamical systems converge ${\alpha}$-exponentially to the unique solution of variational inclusion problems under fewer restrictions imposed on operators and parameters. Several special cases also discussed.
RELATIVE RECIPROCAL VARIATIONAL INEQUALITIES
Khan, Awais Gul,Noor, Muhammad Aslam,Pervez, Amjad,Noor, Khalida Inayat The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.3
In this paper, we introduce a new class of reciprocal convex set which is called as relative reciprocal convex set. We establish a necessary and sufficient condition for the minimum of the differentiable relative reciprocal convex function. This condition can be viewed as a new class of variational inequality which is called relative reciprocal variational inequality. Using the auxiliary principle technique we discuss the existence criteria for the solution of relative reciprocal variational inequality. Some special cases which are naturally included in our main results are also discussed.
MIXED QUASI VARIATIONAL INEQUALITIES INVOLVING FOUR NONLINEAR OPERATORS
( Amjad Pervez ),( Awais Gul Khan ),( Muhammad Aslam Noor ),( Khalida Inayat Noor ) 호남수학회 2020 호남수학학술지 Vol.42 No.1
In this paper we introduce and consider a new class of variational inequalities with four operators. This class is called the extended general mixed quasi variational inequality. We show that the extended general mixed quasi variational inequality is equivalent to the mixed point problem. We use this alternative equivalent formulation to discuss the existence of a solution of extended general mixed quasi variational inequality and also develop several iterative methods for solving extended general mixed quasi variational inequality and its variant forms. We consider the convergence analysis of the proposed iterative methods under appropriate conditions. We also introduce a new class of resolvent equation, which is called the extended general implicit resolvent equation and establish an equivalent relation between the extended general implicit resolvent equation and the extended general mixed quasi variational inequality. Some special cases are also discussed.