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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.
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.
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.
Muhammad Ahmed Farooqui,Muhammad Umar,Muhammad Amjad Sabir,Rashid Pervez,Tarib Jalees 한국지질과학협의회 2019 Geosciences Journal Vol.23 No.2
Detailed geochemical analyses of clastic fraction of the oldest exposed Salt Range Formation in the famous salt producing region (Salt and Trans-Indus Ranges) Pakistan was carried out in order to understand provenance, paleoclimate, depositional and tectonic settings. Sandstone and shale samples of Salt Range Formation were analysed for major, trace and rare earth elements and various geochemical models and ratios were used to interpret. Geochemical analyses of both sandstone and shale fraction mostly display similar results and interpretations. The samples are classified as arkose, subarkose, litharenites and were sourced from felsic and/or intermediate igneous rocks. The sedimentation of the detritus was occurred in fluvial to restricted shelf conditions under arid to semi-arid and oxygenated climate conditions. The tectonic settings of the sediments were mainly Oceanic and Continental Island arcs as well as Active Continental margin.