In this paper, we prove a sufficient condition that every nonempty closed convex bounded pair M , N in a reflexive Banach space B satisfying Opial’s condition has proximal normal structure. We analyze the relatively nonexpansive self-mapping T on M ∪ N satisfying T M ⊆ M and T N ⊆ N , to show that Ishikawa’s and Halpern’s iteration converges to the best proximity point. Also, we prove that under relatively isometry self-mapping T on M ∪ N satisfying T N ⊆ N and T M ⊆ M , Ishikawa’s iteration converges to the best proximity point in the collection of all Chebyshev centers of N relative to M . Some illustrative examples are provided to support our results.
In this paper is suggested an efficient method to solve differential equations. Using quadratic Legendre multi-wavelets approximation method, differential equations are converted into the system of algebraic equations with the help of operational matrix of integration and its product. Some illustrative examples are included to show the efficiency and applicability of the method.
The Binary quadratic negative pell equation 16 80 2 2 − = x y representing a hyperbola is analyzed for its non-zero integer solutions. A few interesting relations among its solutions are presented. Further, employing the solutions of the above equation, we have obtained solutions of other choices of hyperbolas, parabolas and special pythogorean triangles.
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