TITLE MARCH 2012 - Pakistan Academy of Sciences

More documents

Recommendations

Info

8 Variability of Some Differential Operators Implying Starlikeness 9. Padmanabhan, K.S. On sufficient conditions for starlikeness. Indian J. Pure Appl. Math. 32 (4): 543–550 (2001). 10. Ravichandran, V., C. Selvaraj & R. Rajalakshmi. Sufficient conditions for starlike functions of order . J. Inequal. Pure and Appl. Math. 3 (5): Art. 81: 1–6 (2002). 11. Singh, S., S. Gupta, & S. Singh. Starlikeness of analytic maps satisfying a differential inequality. General Mathematics 18 (3): 51–58 (2010).
Proceedings of the Pakistan Academy of Sciences 49 (1): 9-17 (2012) Copyright © Pakistan Academy of Sciences ISSN: 0377 - 2969 Pakistan Academy of Sciences Original Article Some New s-Hermite-Hadamard Type Inequalities for Differentiable Functions and Their Applications Muhammad Muddassar*, Muhammad I. Bhatti and Muhammad Iqbal Department of Mathematics, University of Engineering & Technology, Lahore, Pakistan Abstract: In this paper, we establish several inequalities for some differentiable mappings that are connected with the celebrate Hermit - Hadamard integral inequality for s-convex functions. Also a parallel development is made base on concavity. Applications to some special means of real numbers are found. Also applications to numerical integration are provided. Keywords and Phrases: Hermite-Hadamard type inequality, s-Convex function, p-logarithmic mean, H lder’s inequality, Trapezoidal formula, special means. (AMS SUBJECT CLASSFICATION: 26D15, 39A10 and 26A51) 1. INTRODUCTION Let a function defined as is said to be convex if the following inequality holds For all x, y and t [0, 1]. Geometrically, this means that if P, Q and R are three distinct points on graph of f(x) with Q between P and R, Then Q is on or below chord PR. There are many result associated with convex function in the area of inequalities, but one of those is the classical Hermite Hadamard inequality. for . (1.1) Hudzik and Maligranda [3] considered, among others, the class of functions which are s-convex in the second sense. This is defining as follows. A function is said to be s- convex in the second sense if _____________________ (1.2) Received, December 2010; Accepted, March 2012 *Corresponding author: Muhammad Muddassar; Email: malik.muddassar@gmail.com holds for all and for some fixed s that every 1- convex function is convex. In the same Paper [3] H. Hudzik and L. Maligranda discussed a few result connecting with s-convex function in second sense and some new result about Hadamard inequality for s-convex function is discussed in [2, 7]. On the hand, there are many important inequalities connecting with 1-convex (Convex) function [2], but one of these is (1.1). Dragomir et al [7], proved a variant of Hermit- Hadamard inequality for s-convex function in second sense. Theorem 1. Suppose that is s- convex function in the second sense. Where and let then the following inequality holds. (1.3) The constant is the best possible in the second inequality in (1.3). The inequality in (1.3) becomes reverse when the function is
Page 1 and 2: Vol. 49(1), March 2012
Page 3 and 4: Proceedings of the Pakistan Academy
Page 5 and 6: Sukhwinder Singh Billing 3 To prove
Page 7 and 8: Sukhwinder Singh Billing 5 Corollar
Page 9: Sukhwinder Singh Billing 7 zq( z)
Page 13 and 14: Inequalities for Differentiable Fun
Page 23 and 24: Supra β-connectedness on Topologic
Page 25 and 26: Supra β-connectedness on Topologic
Page 29 and 30: M.K. Aouf et al 27 ∞ ∑ k=2(1
Page 31 and 32: M.K. Aouf et al 29 [1 + |3 − 2β|
Page 33: M.K. Aouf et al 31 Rend. del Circol
Page 36 and 37: 34 Shayma Adil Murad et al Lemma 2.
Page 38 and 39: 36 Shayma Adil Murad et al where As
Page 40 and 41: 34 Shayma Adil Murad et al
Page 42 and 43: 40 Rabha W. Ibrahim (z ) is remo
Page 44 and 45: 42 Rabha W. Ibrahim G( r, ks; z) =
Page 49 and 50: Inclusion Properties of p-Valent Me
Page 57 and 58: Inclusion Properties of Certain Ope
Page 59 and 60: Inclusion Properties of Certain Ope
Page 61 and 62:
Inclusion Properties of Certain Ope
Page 63:
Inclusion Properties of Certain Ope
Page 66 and 67:
64 Citations of Elected Fellows com
Page 68 and 69:
66 Citations of Elected Fellows Dr.
Page 72 and 73:
Proceedings of the Pakistan Academy
Page 74:
OF THE PAKISTAN ACADEMY OF SCIENCES
show all

TITLE MARCH 2012 - Pakistan Academy of Sciences

Create successful ePaper yourself

Delete template?

Save as template?