Abstract. The notion of dualistic Geraghty Contraction is introduced. A new fixed point theorem is proved in the settings of complete dualistic partial metric spaces. The counterpart theorem provided in partial metric spaces is retrieved as a particular case of our new results. We give example to prove that the contractive conditions in the statement of our new fixed point theorem can not be replaced by those contractive conditions in the statement of the partial metric counterpart fixed point theorem. Moreover, we give an application of our fixed point theorem to show the existence of solution of integral equations. AMS Subject Classification: 47H09; 47H10; 54H25 Keywords and Phrases: Fixed point, dualistic contraction, dualistic partial …show more content…
Remark 1.3. It is obvious that every partial metric is dualistic partial metric but converse is not true. To support this comment, define D∨ : R × R → R by D∨(j, k) = j ∨ k = sup{j, k} ∀ j, k ∈ R. It is clear that D∨ is a dualistic partial metric. Note that D∨ is not a partial metric, because D∨(−1, −2) = −1 / ∈ R+. However, the restriction of D∨ to R+, D∨|R+ , is a partial metric. Example 1.4. If (M, d) is a metric space and c ∈ R is an arbitrary constant, then D(j, k) = d(j, k) + c. defines a dualistic partial metric on M. Following [8], each dualistic partial metric D on M generates a T0 topology τ (D) on M which has, as a base, the family of D-open balls {BD(j, ) : j ∈ M, > 0} and BD(j, ) = {k ∈ M : D(j, k) < + D(j, j)}. 74 M. NAZAM, M. ARSHAD AND CH. PARK If (M, D) is a dualistic partial metric space, then dD : M × M → R+0 defined by dD(j, k) = D(j, k) − D(j, j). is called quasi metric on M such that τ (D) = τ (dD) for all j, k ∈ M. Moreover, if dD is a quasi metric on M, then ds D(j, k) = max{dD(j, k), dD(k, j)} defines a metric on M. A sequence {jn}n∈N in (M, D) converges to a point j ∈ M if and …show more content…
Definition 1.5. [8] Let (M, D) be a dualistic partial metric space, then (1) A sequence {jn}n∈N in (M, D) is called a Cauchy sequence if limn,m→∞ D(jn, jm) exists and is finite. (2) A dualistic partial metric space (M, D) is said to be complete if every Cauchy sequence {jn}n∈N in M converges, with respect to τ (D), to a point j ∈ M such that D(j, j) = limn,m→∞ D(jn, jm). Following lemma will be helpful in the sequel. Lemma 1.6. [8, 9] (1) A dualistic partial metric (M, D) is complete if and only if the metric space (M, ds D) is
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All of the above sounds good to me; however I have written a term paper
DMD also known as muscular dystrophy is muscular disease that occurs on young boys around age four to six. Muscular dystrophy is genetically transmitted disease carried from parent to offspring. This disease progressively damages or disturbs skeletal and cardiac muscle functions starting on the lower limbs. Obviously by damaging the muscle, the lower limbs and other muscles affected become very weak. This is ultimately caused by the lack dystrophin, a protein the body produces.
Even though there are many cases and arguments for Dualism concerning mind - body, such as Descartes’ substance dualism, the theory does not often have hard, physical evidence to back up such premise like science does. The continued scientific progress over the past centuries has allowed us to better understand universal truths and the functions of the mind-body that were not able to have been explained scientifically in the past. Many complex, unexplained complexities have been simplified or “reduced” through chemistry,biology, or physics. Through both comparison of arguments supporting dualist theories and counter arguments, I will prove that Dualism is a concept of the past and the continued scientific progress is inevitable and will one day allow us to understand many Dualistic explanations with hard evidence and scientific proof that we have failed to do so in the past.
Dualism is the theory that the mind and body are two separate things. Dualism implies that the mind and soul can exist separate from the actual body. In the mind we have inner states. These states are considered not connected to any specific part of the body but in another place entirely. No one knows that’s why they are considered inner states. Inner states cannot be questioned because we as humans cannot distinguish each and every other persons’ inner thoughts. We can only distinguish our own thoughts and inner states. That is why the argument that
The text "Dueling Dualism" by Anne Fausto-Sterling claim is that sex and gender are constructed. Scientist construct gender and sex through their research and studies and this creates the way society views sex and gender. Sterling writes, "... human sexuality created by scholars in general and by biologists, in particular, are one component of political, social, and moral struggles about our cultures... At the same time... incorporated into our very physiological being... Biologists...in turn refashion our cultural environment"(Sterling,5). Sterling, sure enough, realizes how sexuality is viewed by biologist but also how it can change the perspectives of sexuality in a society. Biologist have "refashion our cultural environment" and are reshaping
Dualism claims that the mind is a distinct nonphysical thing, a complete entity that is independent of any physical body to which it is temporarily attached. Any mental states and activities, as well as physical ones, originate from this unique entity. Dualism states that the real essence of a person has nothing to do with his physical body, but rather from the distinct nonphysical entity of the mind. The mind is in constant interaction with the body. The body's sense organs create experiences in the mind. The desires and decisions of the mind cause the body to act in certain ways. This is what makes each mind's body its own.
Surprisingly dualism has become synonymous with Rene Descartes that often times it is many just referred to by many as Cartesian dualism, as if this was the decisive line of attack to the issue. The theory behind dualism is that the mind and the body, that mind and matter, are two distinct things. Descartes well-thought-out the difficulty of the location of the mind and came to the conclusions that the mind was a completely separate entity from the body. Descartes stated that he is a subject of conscious thought and experience and thus cannot be nothing more than spatially extended matter. The fundamental nature of the human being, or the mind, are unable to be material but are obliged to be no...
My research design was loosely framed within the theories of Vygotsky. The social constructivist work of Vygotsky was centered on understanding of how social interactions lead to conceptual understanding. My study, influenced by Vygotsky’s work, was focused on how students used those social interactions to construct conversations that are meaning-making. My research does not look deeply into how students internalize their social interactions, but rather, in specifically investigate the production of the generative discourse that plays a role in conceptual understanding. My research uses dialogic models of language suggested by Keys et al. (2000). Their research suggests that dialogic models of language are appropriate for conducting research
Sructural functionalism has several major features and criticisms. The major features are social processes, the AGIL scheme, norms and values and the voluntaristic theory. Talcott Parsons received quite a lot of criticism over his ideas. The criticisms I will discuss are conflict theory, feminist criticism, Marxist criticism, rational actor approaches and neo-functionalism. Structural functionalism sees society as a complex system with parts that work together to promote solidarity and stability.
In the article, “Doubts about Doublespeak” by William Lutz addresses the language we call “Doublespeak.” The obscure language that is intended to communicate, without being straightforward. For example, a job companies manager telling employees they are downsizing the company, instead of saying we are firing are few employees. Doublespeak is to tell someone something, without being blunt about it. Even though doublespeak is affecting use, we continue to use it in or everyday lifestyle. Although we may not recognize it social media is one way we continuously use it. In the article Lutz provides four types of doublespeak, euphemism, jargon, gobbledygook, and inflated language. I do agree along with support William Lutz ideas about doublespeak.
Truth tables are a kind of table for describing the set of result for each alternative set of inputs. Using the truth table will help designers to write Boolean expressions more easily. An example of the truth table can be found at Figure 2.3. The output V will be one if two or three of the inputs are one.
Complete the following statements. Note that you are allowed to ONLY use terms from the list below; other terms WILL NOT be accepted. ( 10 MARKS)
Definition 2.1.11 (Valid Positive Rules of Interest)Let for a transactional database D ,set of items are of Interest I and be the itemsets then AB is a valid rule of interest if it satisfies following
The remainder of the paper is organized as follows – first an overview of the relations