ریاست قلات میں نظام قضاء کا تحقیقی جائزہ

In Islam the system of Judiciary halds an immense importance the judiciary after faith is counted as an important obligation amongst all other obligations and is eminent and virtous amongst all outs of worships. The virue of judiciary is mentioned at hundreds of places in the Quran and in the Ahadiths. The Progression of the system of judiciary has been hard from the begning of the prophet hood, during the Rashidun ealiphale and is promulgated till tody. Before the existence of Pakistan there were many states amongst which one was the state of Kalat. Where the Baloch Government was setup in 1530 Meer Ahmed Yar Khan was elected as the Khan of Kalat. Who at the very Beginning laid the foundation of the system of judiciary? The details about this would be discussed in the article ahead. The Government of Balochs was set up in Kalat the foundation of system of judiciary here was first of all laid by Mir Ahmed Yar Khan. First of all juges were appointed in every district.

Harmonically S, M -Convex Functions and Related Inequalities

The theory developed about convex functions, arising from intuitive geometrical observations, may be readily applied to topics in real analysis and economics.Convexity is a simple and natural notion which can be traced back to Archimedes (circa 250 B.C.), in connection with his famous estimate of the value of π (using inscribed and circumscribed regular polygons). He noticed the important fact that the perimeter of a convex figure is smaller than the perimeter of any other convex figure surrounding it. In modern era, there occurs a rapid development in the theory of convex functions. There are sereval reasons behind it: firstly, many areas in modern analysis directly or indirectly involve the applications of convex functions; secondly, convex functions are closely related to the theory of inequalities and many important inequalities are consequences of the applications of convex functions (see [64, 47]). Inequalities play a important role in almost all fields of mathematics. Several applications of inequalities are found in various area of sciences such as, physical, natural, engineering sciences. In numerical analysis, inequalities play a main role in error estimates of different important integrals whom analytic solutions could not be found. In recent years, a number of authors have considered extensions/generalizations of convex functions in various aspects and also tried to build several relations like HemiteHadamard’s inequalities. We introduce different types of convexities and drive more general Hermite-Hadamard’s inequalities. Further, we derive Ostrowski, Hermite-Hadamard and Simpson, Fejer type inequalities. Also, we discuss applications of these classes such that we can estimate the integrals like Rab x ex n dx; Rab sin xnxdx for n ≥ 1 and a, b ∈ (0, ∞) etc without using numerical analysis. In first chapter, we give information about convex functions, Log-convex functions, Quasi-convex functions, (s, m)-convex functions in second sense and Preinvex functions. In second chapter, we consider the class of harmonically convex functions and investigate some relations between harmonically convex and classical convex functions. We define class of harmonically (s, m)-convex functions which unify the different harmonic convexities and establish Ostrowski, Hemite-Hadamard and Simpson, and Fejer type inequalities for this class of functions. In third chapter, we define the classes of the harmonically p-convex functions which is a generalization of convex functions and harmonically convex functions, and harmonically p-quasiconvex functions, and harmonically logarithmic p-convex functions. Further, we investigate relationship between harmonically p-convex, p-convex and classical convex functions. Also, we give a characterization about the relation between harmonically p-convex and harmonically convex functions. Finally, we establish Hermite-Hadamard type inequalities for harmonically p-convex functions, and inequalities for the product of harmonically p-convex functions, and inequalities for harmonically logarithmic p-convex functions. In fourth chapter, we define the class of p-preinvex functions which is generalization of preinvex and harmonically preinvex functions. We also define the notion of p-prequasiinvex and logarithmic p-preinvex functions. Moreovere, we establish Hermite-Hadamard type inequalities when the power of the absolute value of the derivative of the integrand is p-preinvex and we give results for product of two ppreinvex, and logarithmic p-preinvex functions, and Ostrowski’s type for the class of p-preinvex functions. In fifth chapter, we define harmonically (p, h, m)-preinvex functions which is generalization of harmonically preinvex functions such that preinvex and harmonically p-convex functions are its special cases. Next, we introduce the concept of harmonically logarithmic p-preinvex and harmonically p-quasipreinvex functions. Finally, we establish important and interesting results related to these classes of functions.