17. Al-Isra’/The Night Journey
I/We begin by the Blessed Name of Allah
The Immensely Merciful to all, The Infinitely Compassionate to everyone.
17:01
All Glory is to The One WHO took HIS Servant Muhammad for a journey by night,
from the Grand Sacred Masjid in Holy Makkah to the Distant Masjid in Blessed Jerusalem;
the environs of which WE have especially blessed,
so that WE make him see some of OUR Wonders of Almightiness.
Truly HE - HE is All-Listening, and HE is All-Watching.
17:02
And WE granted the Scripture - the Torah - to Moses, and
made it a source of guidance for Descendants of Jacob.
Saying:
‘Do not take anyone - metaphorically or hypothetically - for a guardian other than ME!
17:03
You are all descendants of those whom WE carried in the Ark with Noah.
He was truly a grateful servant!’
17:04
And WE warned Descendants of Jacob about OUR Decision in their Scripture:
‘You will definitely create and promote corruption in the land twice, and
you will indeed exalt yourselves’ with haughtiness and become grossly overbearing.
And thus you will be punished twice.
17:05
So when the first of these two warnings came true - as the Descendants of Jacob were tuned to sinful disobedience;
WE raised against you OUR servants, people of great power - the Babylonians.
And they ravaged your homes and caused havoc throughout the land.
And it was thus a warning fulfilled!
17:06
Then WE returned to you another chance of victory against them after you had repented,
and strengthened you with wealth/prosperity and sons/manpower,
and made you even more numerous in soldiery than ever.
...
The Quran describes itself as a book of guidance. Sura l-Baqarah, verse (67) states: قَالَ أعُوْذُ بِاللّٰہِ اأنْ أَکُوْنَ مِنَ الْجَھِلِیْنَ۔He said, "I seek refuge in Allah from being among the ignorant. "The Qur'an does not render a coordinated description of the universe Creation and how it will end. In lieu of a continuous story of creation and cease, there are verses dispersed all over the Quran which deal with certain aspects of the universe’s Creation and end. These scattered verses provide information on the sequential events marking its development with varying degrees of detail. The primary objective of this paper is to analyze the Quranic Concept of Universe. The idea of steady state by Hermann Bondi, Thomas Gold, and Fred Hoyle (1948) suggests that this universe is created with big bang, it is expanding and it would be the same, always static, always contracting or always expanding with no end. This is in contrast with the pulsating theory of the accelerating expansion will result in weak gravity which will cause the universe to contract. When this contraction will condense everything back into one single point, this rapid compression will lead to another explosion (often referred to as mini big bang). As a result of which the universe will start expanding again. Hence it results in a pulsating universe in which there is alternate expansion and contraction of universe.
“Behind every theorem lies an inequality”. Mathematical inequalities play an impor- tant role in almost all branches of mathematics as well as in other areas of science. The basic work ”Inequalities” by Hardy, Littlewood and Polya appeared 1934 [37]and the books ”Inequalities” by Beckenbach and Bellman published in 1961 [9] and ”An- alytic inequalities” by Mitronovic published in 1970 made considerable contribution to this field and supplied motivation, ideas, techniques and applications. This theory in recent years has attached the attention of large number of researchers, stimulated new research directions and influenced various aspect of mathematical analysis and applications. Since 1934 an enormous amount of effort has been devoted to the dis- covery of new types of inequalities and the application of inequalities in many part of analysis. The usefulness of Mathematical inequalities is felt from the very be- ginning and is now widely acknowledged as one of the major deriving forces behind the development of modern real analysis. This dissertation deals with the inequali- ties for Jensen inqualites involving average of convex functions, Hermite-Hadamard inequalities. Chapter 1 offers an overview of the basic results contains a survey of basic concepts, indications and results from theory of convex functions and theory of inequalities used in subsequent chapters to which we refer as the known facts. Chapter 2 we give proofs of convexity and Schur convexity of the generalized inte- gral and weighted integral quasi-arithmetic mean. An overview of assorted proofs of schur convexity of integral arithmetic mean is discussed. In a detailed proof, discrete Jensen inequality for integral arithmetic mean is derived. Also integral version of Jensen inequality for integral arithmetic mean is proved. Motivated by discrete and viiviii integral Jensen inequalities functionals are defined. Two different method is given for constructing new examples of exponentially convex functions from non trivial gen- erating families of functions. Mean value theorem are proved. Different classes of monotonically increasing Cauchy means are created. Chapter 3 gives us convexity and Schur convexity of functions connected to Hermite- Hadamrd inequality as well as Schur convexity of differences of Hermite-Hadamrd inequality and Hammar-Bullen inequality by different proofs. Applying assorted gen- eralizations of Hermite-Hadamard inequality and Hammer-Bullen inequality on some special families of functions from varied classes, n-exponentially convex functions are generated by quite new method. Lyponuve, Dresher and Gramm’s type inequalities are developed. Pretty different Stolarsky type means are derives preserving inherited monotonically increasing property. Chapter 4 deals with inequalities of higher order convexity and divided difference. Two of them use majorization results and others are related to Jensen inequalities and Hermite-Hadamrd inequality. Integral Jensen inequality for divided difference is proved. Applications of averages of 3-convex functions as first order divided difference of convex functions are acquired. Method of producing n-exponentially convex func- tions is applied using divided differences. Produced functions are used in studying Stolarsky type means In the fifth chapter results about averages values of convex func- tions with variable limits and average values of composition functions is given. Study functionals for inequalities proved by D.E. Wulbert ( call them Wulbert’s inequalities for convenience) for convex and three convex functions. Extensions, improvements are accomplished. Variety of Stolarsky type means of a concave (convex) functions are obtained.