In this paper, we obtain some fixed point results for generalized weakly contractive mappings with some auxiliary functions in the framework of b-metric spaces. The proved results generalize and extend the corresponding well-known results of the literature. Some examples are also provided in order to show that these results are more general than the well-known results existing in literature. MSC: Primary 47H10; secondary 54H25
We introduce some new contractions on intuitionistic fuzzy metric spaces, and give fixed point results for these classes of contractions. A stability result is established.
The aim of this paper is to present fixed point results of multivalued mappings in the framework of partial metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. As an application of our main result, the existence and uniqueness of bounded solution of functional equations arising in dynamic programming are established.
The paper proposes an application of an optimization evolutionary technique, improved Differential Evolution, to reactive power planning. This problem could be formulated mathematically as a nonlinear, non smooth, mixed integer, multi-objective optimization problem. The main objective deals with the minimization of the real power losses that result in a better reactive power dispatch and improving the voltage profile across the system and keeping the control variables in their operational limits. Here we use an approach to deal with discrete variables, Mixed Integer Hybrid Differential Evolution (MIHDE), a modified Differential Evolution algorithm.The proposed approach has been tested in a modified version of two electric networks, the Nordic 32, 60 bus and IEEE 118 bus system.
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