MANAJEMEN PENDIDIKAN ISLAM DI PESANTREN: PERSPEKTIF EPISTEMOLOGI

Management of Islamic education in pesantren needs to return to its historical roots in order to confirm the identity, character, distinctiveness and uniqueness. There is a spirit that is timeless, even the underlying model of ideal education in the contemporary era. Development of Islamic epistemology for education should be able to give birth to a generation of Muslims who worships in the field of religion and experts in the field of science and technology. Pesantren as an educational institution of Islam with a good management should be able to play its role to achieve this goal. Whereas in fact there who think that pesantren have not been able to put its strategic position in the development of science in accordance with the times. Nevertheless, the existence of Islamic educational institutions such as pesantren is evidence that pesantren have been organized in a good management so that it can survive in changing times from time to time. More precisely knowing Islamic education management in pesantren from the perspective of epistemology may illustrate that pesantren will continue to be needed to confront the changing times.

On Functions With Nondecreasing Increments

In last few decades, the concept of functions with non-decreasing increments got attention of many mathematicians due to its worth and importance. We would like to establish a connection/relation among functions with non-decreasing increments and arithmetic integral mean, Wright convex functions, convex functions, r?convex functions, Jensen m?convex functions, m?convex functions, m ? r?convex functions, k?monotonic functions, absolutely monotonic functions, completely monotonic functions, Laplace Transform and exponentially convex functions, by using thenite di erence operator as di erent cases ofm h f. We also consider function with nondecreasing increments of third order and get the generalisations of the Levinson''stype inequality and Jensen-Mercer''s-type inequality by using Jensen-Boas inequality. We will deduce some general identities of Popoviciu type for discrete case for sums for function and sequence in two dimension using higher order r divided difference, positivity of these expressions are characterised for higher order r?convex functions. We will also obtain some general identities of Popoviciu type for integral R R P(y; z)f(y; z)dy dz of higher order di erentiable function and positivity of these expressions are characterised for higher order r?convex and completely monotonic functions. We would discuss some applications in terms of generalised Cauchy-type means and exponential convexity as well. We would get the generalisation of discrete identity and inequality ofCeby sev-type and discuss generalisation of integral identities and inequalities ofCeby sev-type and K. Fan-type for higher order r?convex functions with two variables. Further, we will obtain double weighted integrals Montgomery''s identities and using these identities we deduce generalisation of Ostrowski- and Gr uss-type inequalities for double weighted integrals for di erentiable functions of higher order with two variables.